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Logic Versus Approximation

Essays Dedicated to Michael M. Richter on the Occasion of His 65th Birthday

Nowadays knowledge-based systems research and development essentially employs two paradigms of reasoning. There are on the one hand the logic-based approaches where logic is to be understood in a rather broad sense; usually these approaches are used in symbolic domains where numerical calculations are not the core challenge. On the other hand we find approximation oriented reasoning; methods of these kinds are mainly applied in numerical domains where approximation is part of the scientific methodology itself. However, from an abstract level all these approaches do focus on similar topics and arise on various levels such as problem modeling, inference and problem solving techniques, algorithms and mathematical methods, mathematical relations between discrete and continuous properties, and are integrated in tools and applications. In accordance with the unifying vision and research interest of Michael M. Richter and in correspondence to his scientific work, this book presents 13 revised full papers advocating the integration of logic-based and approximation-oriented approaches in knowledge processing.

Problem-specific algorithms vs. heuristics, exact optimization vs. approximation
vs. heuristic solutions, guaranteed run time vs. expected run time vs.
experimental run time analysis. Here, a framework for a theory of randomized
search heuristics is presented. After a brief history of discrete optimization,
scenarios are discussed where randomized search heuristics are appropriate.
Different randomized se- arch heuristics are presented and it is argued why the
expected optimization time ...